Here is my scenario. I want to implement A* (in Python) without having to resort to linear-time min or in operations. I need a heap to be able to efficiently get the lowest weight item.
My immediate response was 'Easy! I'll use heapq!' Then I discovered that life is rarely as simple as we would like it to be. It turns out that this strategy is suboptimal for one of the crucial points of A*. When consider children, I need to occasionally update the scores of the children already on the heap.
For those whose memory of A* has lapse a little, the gist of it is that I want to take an element, modify its weight, and modify the heap to reflect the change, all in sub-linear time.
Any suggestions?
For complexity purposes, you would want to try a binomial or Fibonacci heap; it appears that there are implementations of both in Python but not production-grade libraries. A binary or d-ary heap might work faster in practice, though. The heapq page mentions how to do updates (keep a reference to the item that you insert into the heap, mark it as invalid and then insert a new version). There are faster algorithms for maintaining the heap property after updates, though. Look at http://en.wikipedia.org/wiki/D-ary_heap for the algorithms to use for fast updates, but you would probably need to implement your own heap on top of an array for those.